Stable FDITD formulation for electromagnetic field diffusion in soft magnetic materials

In this paper, a stable finite difference discretization is defined for problems of electromagnetic field diffusion in nonlinear hysteretic media. More precisely, the numerical formulation consists of a Crank-Nicolson-like algorithm applied to a space-centered finite difference scheme for nonuniform point distribution. Following the von Neumann analysis, the unconditional stability of this implicit two-level/three-point scheme is established. Moreover, the good behavior of this formulation has been numerically verified for very critical soft material like ferrites and irons.